ELEMENTARY ALGEBRA - MWCC

ELEMENTARY ALGEBRA

Overview

The Elementary Algebra section of ACCUPLACER contains 12 multiple choice Algebra questions that are similar to material seen in a Pre-Algebra or Algebra I pre-college course. A calculator is provided by the computer on questions where its use would be beneficial. On other questions, solving the problem using scratch paper may be necessary. Expect to see the following concepts covered on this portion of the test:

Operations with integers and rational numbers, computation with integers and negative rational numbers, absolute values, and ordering are included.

Operations with algebraic expressions that must be solved using simple formulas and expressions, adding and subtracting monomials and polynomials, multiplying and dividing monomials and polynomials, positive rational roots and exponents, simplifying algebraic fractions, and factoring.

Operations that require solving equations, inequalities, and word problems, solving linear equations and inequalities, using factoring to solve quadratic equations, solving word problems and written phrases using algebraic concepts, and geometric reasoning and graphing.

Testing Tips

Use resources provided such as scratch paper or the calculator to solve the problem. DO NOT attempt to only solve problems in your head.

Start the solving process by writing down the formula or mathematic rule associated with solving the particular problem.

Put your answer back into the original problem to confirm that your answer is correct. Make an educated guess if you are unsure of the answer.

Algebra Tips

Test takers should be familiar with the following concepts. For specific practice exercises using these concepts, please utilize the resources listed at the end of this guide.

Understanding a number line Adding and subtracting negative numbers Using exponents Finding a square root Writing algebraic expressions Using parentheses in algebraic expressions Evaluating formulas

Multiplying binomials Using proportions to solve problems Combining like terms Evaluating expressions Solving linear equations Solving equations

Practice Questions

Order of Operations

1. 372

3. 42 2 (4 2

2. 3 257

Please note: Multiplication signs

may take the form of an x, *, or ?

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Scientific Notation

Write the following in Scientific Notation. Write in expanded form.

1. 0.0000000000523

2. 6.021011

Simplify. Write answers in scientific notation.

1. 3103 5106

2. 6 109 3104

Substitution Find each value if x 3, y 4, and z 2.

1. xy z4z

2. 5x z xy

Linear equations in one variable

Solve the following for x. 1 . 6x486

2. 50x 3x20

Formulas

1. Solve PV nRT for T.

2. Solve y hx4xfor x.

Word Problems

1. One number is 5 more than twice another number. The sum of the numbers is 35. Find the numbers.

2. Sheila bought burgers and fries for her children and some friends. The burgers cost $2.05 each and the fries are $.85 each. She bought a total of 14 items, for a total cost of $19.10. How many of each did she buy?

Inequalities

Solve and graph on the number line. 1. 2x7 3

2. 3x 4x 112

Exponents & Polynomials

Simplify and write answers with positive exponents.

1. 3x2 5x 65x2 4x 4

2. 24x4 32x3 16x2 8x2

3. 5a 6

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Factoring

1. x2 5x 6

2. 2x2 4x16

3. 4x2 36

4. 49y2 84y 36

Quadratic Equations Solve:

1. 4a2 9a2 0

2. 3x2216

Rational Expressions Perform the following operations and simplify where possible. If given an equation, solve for the variable.

1. 4 3a 2a 2 a2 a

Graphing

2. 16x2 x22x8

x22x8

4x2

Graph each equation on the coordinate axis.

1. 3x2y = 6 2. x 3 3. y 2 4. y -2x + 5

3

Systems of Equations

Solve the following systems of equations.

{2x 3y 1 2

1. x 2y 9 Radicals

{2x 3y 4

2. y 2x 4

Simplify the following using the rules of radicals (rationalize denominators). All variables represent positive numbers.

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Answers

Order of Operations 1. 147

2. 3 257 3 107 137 6

3. -9

Rule 1: Simplify all operations inside parentheses.

Rule 2: Simplify all exponents, working from left to right.

Rule 3: Perform all multiplications and divisions, left to right.

Rule 4: Perform all additions and subtractions, left to right. To help remember the order of operations, use the mnemonic To help remember the order of operations, use the mnemonic PEMDAS, which stands for Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction).

Scientific Notation All numbers in scientific notation have the following form: Nonzero digit. Rest of number 10power.

1. 0.0000000000523 5.23 10

2. 602,000,000,000

Substitution

1. xyz -4z = (3)(-4)(2) -4(2) = -24-8=-32

2.5- = 5(3)-(2) = 125-2 = 123 = - 123 = - 41

(3)(-4)

-12 -12

12

4

Linear equations in one variable

Formulas

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Word Problems 1. Let "one number" =2x + 5 if we let "x" = "another number" Remember, sum means to add.

There for the two numbers " 2x + 5" and "x" must add up to 35. So let (2x + 5) + (x) = 35 therefore x = 10 which is "another number." 2x + 5 = 25 which is "one number." So the numbers are 10 and 25. 2. Let x = the number of burgers. Since ther are only 14 items, the rest of the items, 14 ? x, must = the number of fries. To get the total amount of money spent, multiply the number of items by the cost of the item. 2.05 x = the total dollars spent on burgers and .85 (14 ? x) = the total dollars spent on fries. The equation is: 2.05x + .85 (14 ? x) = 19.10. Solving the equation, x = 6. Hence, she bought 6 burgers and 8 fries. Inequalities Solve inequalities the same as equations with one exception. When both sides are multiplied or divided by a negative number, remember to switch the direction of the inequality. Graph a closed circle if the number is included and an open circle if the number is NOT part of the solution.

Exponents & Polynomials

Factoring Steps to factoring, the FOIL method:

1. Always factor out the Greatest Common Factor (if possible). 2. Factor the first and last term. 3. Figure out the middle term by checking combinations of the Inner and Outer terms.

1. x2 5x6 x 6x 1, to check, multiply back using FOIL method

2. 2x2 4x16 2(x2 2x8) 2(x- 2) (x 4)

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